Labour leader Alan Kelly says officials should look at accelerating the easing of some restrictions if the rate of coronavirus infection continues to decline.
However, he says reopening non-COVID parts of the health service that have been temporarily suspended should be a priority.
Earlier, the Taoiseach said a decision on moving to phase two would be made on June 5th.
Leo Varadkar indicated the Government would first need to see data on the effect of the recent loosening of some restrictions.
It comes as the number of new cases remains below 100 for the sixth day in a row, and a continuing fall in hospital and ICU admissions.
Speaking on The Hard Shoulder, Labour leader Alan Kelly also said it's important to see the numbers that emerge next week following that initial easing of restrictions.
Deputy Kelly said: "If the trends continue in the positive way, I certainly believe that we have to consider bringing forward some aspects.
“We also have to bring forward the roadmap for opening up health services.
“We know when pubs are going to open, but we don’t know when women and men are going to be screened for cancer - that shows a problem with our priorities."
Deputy Kelly also discussed the recent advice suggesting TDs should only spend two hours in the Dáil chamber per day.
The Court Service had moved to introduce a similar time limit, although has now confirmed full sittings are expected to resume as early as tomorrow.
Deputy Kelly said he's now seen other advice that suggests the two-hour time limit wouldn't be necessary if other hygiene and social distancing measures are observed.
In terms of the current limit, the Labour leader observed: “If this is the case in a confined room like the Dáil, surely this is a similar issue for other works in other places across the whole country?
“From a small business point of view, it would be virtually impossible to adapt what we are doing in the Dáil today onto their business - it would make it unviable. It would make factories very untenable.
“How can we have a situation like George Orwell had in Animal Farm - a situation where some are more equal than others?"
He said the Oireachtas should now go back to the same situation as a week ago, before the latest advice was issued and implemented.
He told Ivan: “We have lost a session with a minister today… we’re restricted in our times going into the Chamber… we’ve had the COVID committee change how it was doing its work.
“This idea that there’s a huge risk for two hours within 24 hours, in any way, shape or form, needs to be re-looked at."